@Goldenzeal Oh, no, reading each others thoughts, that's what discussion is about. 😜 Though, I'll apologise if you'd think my language was crude, but please don't mind me, I just have a filthy mouth. Well, anyway, the final response then...
You are born either the child of a noble, or not. As the child of one, you'll be sent to train under a knight as a squire. You are technically not a noble at this stage, but recognized as a noble son. After you come of age, you'll become a fully fledged knight and officially a noble of the realm, then when your father passes, you'll receive whatever he left for you. As a second or third child, if your father have the money, you too will be trained as a squire and get the chance of gaining your knighthood, becoming a noble. If not, you will become a freeman or commoner. That's why, being a knight is the baseline.
They did not take part in court because they were too low in the peerage system. As I've said, they're glorified guards, as far as social status goes. You're not going to bring in a supervisor into a discussion among the board of directors, no matter how useful or valid that supervisor might be.
Climbing up the social rank in medieval times is not just hard, it's downright impossible, because it's entirely based on bloodline and relations. Wealth is based on land, because everyone (including kings) were money poor. That's why lands were given away as income. It is also why so many jump at the Crusades, because it is one of the few moments in history where you can actually rise above your station with merit, and that most lands were already taken back in Europe.
you are correct that the lords usually lead the armies themselves, but the "men at arms" were almost always landed knights so.... you kinda proved yourself wrong there...
How did I proved myself wrong? The knights belong to the Lord they are under. The land, which the knights own, are their salary for their service, given to them by their Lord, and is located within the Lord's domain. The Lord is in turn, one of the upper echelon leading the country and his domain, is his salary. Also, the majority of men-at-arms were actually not knights, because knights were expensive, so knights tend to act as squad leaders, or captains and the like. That's why I estimated them to be lieutenants, and even in the Napoleonic era, the 'knight's' equivalent rank was around lieutenant.
It's like you hiring a maid with your salary. Your maid is not going to have a say on how you run your household, let alone going to your workplace and advising how to run things over there. That is how low a knight ranks in the peerage system. Also, fun fact: Lady-in-waiting, female servants of nobility (maids, really), are almost all of noble birth, and their male counterparts? Knights.
you are missing out on the entirety of the merchant class as well as the free peasants who were the once who paid the majority of the tax
Actually, no. The majority of tax in the medieval era is from serfs, in the form of wheat, then mostly labour and a little money or whatever, from the artisan or commoners. Freemen farmers, too paid in harvest, but they and the merchant class are a minority. Money poor, remember. It is only towards the Renaissance period that the middle/merchant class begin to increase.
It is also this Renaissance era that the Sun King of France was the first to switch from a feudal system to an absolute monarchy, where all Lords were deprived of their military right. Lord's then only need pay taxes to the crown and only the king is allow to muster armies. Of course, the Lords were quite happy about it, since they no longer need to go onto the battlefield themselves. This also shows the extend of a Lord's military authority, before this time period.
Anyway, yeah, too troublesome to dig for sources... so, cheers, mate.